Device and method for teaching numeral systems

ABSTRACT

A device and method of teaching and learning numeral systems comprising at least one game board and a plurality of value block pieces, wherein the game board comprises columns whereby one column is a decimal point column and other columns are each a numeric column to form a numeric grid thereon, and wherein each value block piece identifies the number equivalent value of a numeric symbol derived from the symbol&#39;s location on the numeric grid.

FIELD OF THE INVENTION

The present invention relates to a device and method comprising a gameboard with accompanying game pieces for use in learning and teachingnumeral systems.

BACKGROUND OF THE INVENTION

There are available a wide variety of devices having numbers imprintedupon their surfaces for the purpose of teaching young learners placevalue, rounding, and naming numbers. Despite the availability of thosedevices, there still is a need, particularly for young learners to learnnumeral systems, have an intuitive feel for the denary numeric symbols,understand formation and partitioning of whole numbers and decimalnumbers, determine rank order of numbers and understand how todifferentiate between numeric symbols and numbers which can be formedfrom those symbols.

SUMMARY OF THE INVENTION

Accordingly, it is one object of the present invention to provide adevice and method for teaching and learning numeral systems withemphasis on the most commonly used denary (base 10) numeral system.

It is another object of the present invention to provide a device andmethod for teaching and learning the numeric symbols “0”, “1”, “2”, “3”,“4”, “5”, “6”, “7”, “8” and “9” which are used for the denary numeralsystem and other numeral systems that have different base indices.

It is yet another object of the present invention to provide a deviceand method for teaching and learning the formation and partitioning ofwhole numbers and decimal numbers.

It is yet another object of the present invention to provide a deviceand method for teaching and learning how to determine the rank order oftwo or more numbers.

It is yet another object of the present invention to provide a deviceand method for teaching and learning how to differentiate betweennumeric symbols and numbers which can be formed by those symbols.

These and other objects of the invention are achieved by providing adevice and method that teaches the “countable value” of each numericsymbol as it appears in a sequence of combined numeric symbols,inclusive of a decimal point, thereby teaching and learning counting andsynthesis of disparate and unobvious aspects of the numeral systems.

When used for sequential counting, this invention aids users tovisualize number in geometric units as “linear distance from zero” (e.g.the number nine is visually the linear distance between zero-and-nine).There is equal spacing between consecutive linear distances (1, 2, 3etc). As an illustration of addition and multiplication, the distancebetween zero-and-three added to another distance between zero-and-threeis equivalent to the distance between zero-and-six (3+3=6 or 3×2=6).Extending this illustration to subtraction, a comparison ofzero-and-three vs zero-and-four is visually the linear distance betweenthree-and-four (4−3 or 3−4), which by visual comparison is the lineardistance between zero-and-one (+1) or one-and-zero (−1) depending onorientation.

One object of the present invention provides a device and method forteaching and learning numeral systems by teaching that the comparisonsof two or more linear distances form the basis of positive numbers,negative numbers, addition, subtraction and multiplication by wholenumbers. In one embodiment, the invention provides a method and devicefor teaching and learning addition and multiplication. In anotherembodiment, the invention provides a method and device for teaching andlearning subtraction.

As a game, this invention can be played in different game versions.

It is another object of the invention to provide a device and method forincreasing the pace with which a person can develop their understandingof the denary numeral system.

It is another object of the invention to provide a device and methodwhich deepens its users' recognition of different written formats toexpress number, including common language words used to describe number.

Yet another object of the present invention is to provide a device andmethod for teaching and learning numeral systems which teaches that awhole number or decimal number is a collation of denary numeric symbols,each distinct numeric symbol in the collation having a unique numbervalue. For clarity purposes, the number 13002.35 has seven distinctnumber values.

In a preferred embodiment, the device and method of the presentinvention teaches that, for any given whole number or decimal number,one and only one numeric symbol can represent its place value. Forclarity purposes, each of the seven distinct numeric symbols in thenumber 13002.35 has a unique place value.

In another preferred embodiment, the device and method of the presentinvention teaches that the actual formation of numbers is “mechanicallycounted” from right to left. A device can be constructed and mountedonto the game board to illustrate the counting mechanism as orderly,chronological shifts of the numeric symbols as evidenced by the numericgrid.

Over time, users of the invention will progress towards an everincreasing spatial understanding of the “geometry of number” and itsinterface with arithmetic.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a denary numeral system game boardaccording to one embodiment of the invention.

FIG. 2 is a one dimensional illustration of one hundred pieces of threesided value blocks that coincide with the denary numeral system.

FIG. 3 is a one dimensional illustration of one hundred pieces of sixsided cuboid value blocks that coincide with the denary numeral.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The device of the present invention comprises at least one game boardand a plurality of value block pieces, wherein the game board comprisescolumns whereby one column is a decimal point column and the othercolumns are each a numeric column to form a numeric grid thereon, andwherein each value block identifies the number equivalent value of anumeric symbol derived from the symbol's location on the numeric grid.

In a most preferred embodiment, illustrated in FIG. 1, there are sevennumeric columns to the left of the decimal point column on the gameboard and three numeric columns to the right of the decimal point columnEach numeric column has ten rows, the first row of which has insignia“0” representing the numeric symbol 0; the second row “1”; the third row“2”; the fourth row “3”; the fifth row “4”; the sixth row “5”; theseventh row “6”; the eighth row “7”; the ninth row “8”; and the tenthrow “9”. A preferred game board is in no way constrained as to thenumber of columns to the right of the decimal point or to the left ofthe decimal point. Similarly, the game board may also consist of numericsymbols written in the negative (i.e. “−1”, “−2”, “−3”, “−4”, “−5”,“−6”, “−7”, “−8” and “−9”) which could help to distinguish negativenumbers from positive numbers. Likewise, the game board is notrestricted to the number of rows bearing in mind, for example, that thenumber of rows is proportionally related to the base index that is beingrepresented by the game board. A feature of a preferred game board isthat it has equal spacing between the numeric symbols to draw particularattention to the spatial and geometric dimensions of number.

The description label for each numeric column is the place valueposition relative to the decimal point column and is written on thenumeric grid above the insignia for the numeric symbols. In a preferredembodiment of the game board, the description labels for the ten numericcolumns are from left to right: “unit millions place”; “hundredthousands place”; “ten thousands place”; “unit thousands place”;“hundreds place”; “tens place”; “units place”; “tenths place”;“hundredths place”; and “thousandths place”. In cases where the gameboard is adapted for a numeral system other than the denary numeralsystem, alternative description labels should be applied, the details ofwhich depend on the numeral system being employed.

The standard number label for each numeric column is also the placevalue position relative to the decimal point column and is written onthe numeric grid above or below the insignia for the description labels.In a preferred embodiment of the game board, the standard labels for theten numeric columns are from left to right: “10⁶ place”; “10⁵ place”;“10⁴ place”; “10³ place”; “10² place”; “10¹ place”; “10⁰ place”; “10⁻¹place”; “10⁻² place”; and “10⁻³ place”. For clarity, 10⁶ represents thevalue 1000000 and likewise 10⁻² represents the fraction (1/10²) or(1/100). In cases where the game board is adapted for a numeral systemother than the denary numeral system, alternative standard number labelsshould be applied, the details of which depend on the numeral systembeing considered. As an example, if the game board is used for Base 8,the “10⁶ place” would be replaced by the “8⁶ place”. As another example,if the game board is used for Base 5, the “10⁻³ place” would be replacedby the “5⁻³ place”. Thus, the value block pieces that accompany a gameboard depend on the Base numeral system being used by the game board.

The game board can be extended to other base systems. In one embodiment,the numeric grid could be truncated (or extended) to include only thosenumeric symbols that are relevant for other numeral systems. As anexample, Base 3 would only use “0”, “1” and “2”. Base 4 would only use“0”, “1”, “2”, and “3”. Base 6 would only use “0”, “1”, “2”, “4” and“5”. These examples are chosen to illustrate that the invention could beused to teach the counting mechanism of the 24 hour clock. Both 60seconds and 60 minutes use Base 6 and Base 10 simultaneously. 24 hoursuses Base 3 and Base 4 simultaneously. Witness all of Base 3, Base 4,Base 6 and Base 10 at same time at 23:59.59 (i.e. just one second beforemidnight). To extend to numeral systems higher than Base 10, it may beadvantageous to use alpha symbols in addition to the most commonlyrecognised denary numeric symbols so that the teaching and learningderived from the device is not complicated or become convoluted.

The number of value block pieces that are used for a game board dependson the Base numeral systems used in the game board. In a preferredembodiment of the game board, there are one hundred value block piecesin number to accompany it considering that each column is Base 10 andthere are 10 columns being employed. In the case of the 24 hour clockexample, optimally there are 39 value block pieces (10 value blocks eachfor the two Base 10 columns, 6 value blocks each for the two Base 6columns, 4 value blocks for the one Base 4 column and 3 value blocks forthe one Base 3 column).

In one embodiment, the value blocks are three-sided pieces as shown inFIG. 2.

Each value block piece identifies the number equivalent value of anumeric symbol derived from the symbol's location on the numeric grid.In a preferred embodiment, the value block piece is a cuboid having afirst side, second side, third side, fourth side, fifth side and sixthside. As shown in FIG. 3, the first side of each cuboid value block hasinsignia “0”, “1”, “2”, “3”, “4”, “5”, “6”, “7”, “8” or “9”. For eachcuboid value block, the second side is opposite the first side and iseither left blank for game purposes or printed thereon another insigniato draw collective appeal (or individual appeal as the case may be) tothe value block pieces. The third side of each value block has writtenin number language words the place position (i.e. numeric column) of thenumeric symbol. The fourth side which is opposite to the third side ofeach value block is the value of the numeric symbol written as a decimalnumber. The fifth side of each value block is the value of the numericsymbol written in standard form. The sixth side of each value block isthe value of the numeric symbol written as the numeric symbol multipliedby (or divided by in the case decimals) the ordinary number expansion ofthe standard form label.

In a preferred embodiment, users of the invention are to recognize thatthe first side (i.e. the numeric symbol in itself) of every value blockdoes not have numerical value. Further, users of the invention are torecognize that it is the third side (i.e. the place position) of everycuboid value block that gives number substance to the numeric symbol.Moreover, the value blocks in a preferred embodiment are designed toenable its users to draw connections between the fourth, fifth and sixthsides and to recognise that these three sides are different numericalexpressions of the same number and as such have equivalent value.

The entire device may be constructed of wood, for an improvedappearance, or it may even be economically constructed from hard plasticor other polymer. It may even be constructed entirely from cardboard andpaper composite products for a very inexpensive version of the device.

A wide variety of colors may be used to represent the numbers and otherinsignia on the device, as well as the background for the numbers andother insignia, as long as there is sufficient disparity in colorationbetween the background and the numbers and other insignia printedthereupon.

The game element of the entire device can be played in differentversions. One version teaches how to bridge early stage counting withplace value by activating systematic, mechanical movements of thenumeric symbols. In this version, the referee instructs the contestantto collect each value block and turn it so that its top face shows onlythe number words (i.e. the third side of every value block). The refereeasks the contestant to use the words to identify all of the value blocksthat belong on the right of the decimal point column Once the refereeconfirms that the contestant has chosen the correct value blocks, he orshe takes those value blocks and puts them aside.

Then, the referee informs the contestant that the remaining value blocksrepresent whole numbers at which point the contestant is asked toexplain what a whole number is to the best of his or her ability. Thereferee instructs the contestant to group the whole number value blocksaccording to their number words. Once the referee confirms that thecontestant has placed each value block in its correct group, the refereeinstructs the contestant to “order”! Looking only at the words, thecontestant forms a straight line for each group of value blocks.

The referee instructs the contestant to “line”. The contestant mustidentify the correct numeric column for each group of value blocks. Onegroup at a time, the contestant positions the straight line of valueblocks on the numeric grid in its rightful numeric column before turningover each value block so that its top face is showing a numeric symbol.The straight line is then re-arranged in ascending order from “0” to“9”.

The referee instructs the contestant to “ladder”. All value blocks areturned over so that their top faces are blank. The contestant says zero.The referee checks that the right-most numeric symbol “0” is shown. Allother value blocks are blank. The contestant says one and the refereechecks that the right-most numeric symbol “1” is shown with all othervalue blocks blank , . . . , the contestant says thirteen and only theright-most numeric symbols “1” “3” are shown adjoined together as 13,etc.

A second version of the game can be played by two or more people. Eachplayer will take a turn being a contestant and a referee. The playerwith the highest points total wins the game.

In this version, each contestant starts with a score of five points. Thereferee instructs the contestant to initiate round 1 of the game bycollecting all ten value blocks from the “thousandths” numeric columnThe contestant closes his or her eyes and throws the ten value blocksunto the floor. The referee places on the numeric grid, blank face up intheir rightful places, those value blocks whose top face is neither ablank nor a number word. The other value blocks are handed to thecontestant to throw again. This process is repeated until only one valueblock (i.e. “secret count”) remains and revealed for the contestant toplace on the numeric grid. The referee writes down the contestant'ssecret count for the round.

Rounds 2 through 10 are played in the same manner as round 1, eachsuccessive round being played one numeric column to the left of theprevious round. When all ten rounds are finished, the contestant'ssecret counts are written down and the players rotate turns. The scoresare tallied when all contestants have played rounds 1-10. Points areawarded for the highest number in each round. The number created in around takes into account the results from previous rounds! One point isawarded to the contestant with the highest number in each roundrepresenting the “thousandths”, “hundredths” and “tenths”. Three pointsare awarded to the contestant with the highest number in each roundrepresenting the “units”, “tens” and “hundreds”. Four points are awardedto the contestant with the highest number in each round representing the“unit thousands”, “ten thousands” and “hundred thousands”. Six pointsare awarded to the contestant with the highest number after round 10representing “unit millions”.

A third version of the game can also be played by two or more people.The players will alternate turns being a contestant and a referee. Thisversion is geared towards those who are developing their basic numberskills. This version does not require score keeping so players are freeto choose their own scoring system.

In this version, the contestant places all of the value blocks on thefloor with their top face showing the denary numeric symbol. The refereerandomly thinks of a number and either calls it aloud, writes it down inwords or both. Without regard to the unique values of the value blockpieces, the contestant finds the numeric symbols that represent thereferee's number and places them on the numeric grid (where thedescription labels are). The referee and contestant will then deliberateon their efforts. The referee may request an independent player tochallenge the contestant on the accuracy of the assembled number.Similarly, the contestant may request an independent player to challengethe referee on the accuracy of the spoken or written number. Once theresults have been validated and agreed by all parties, the playersrotate the referee and contestant. Over time, both players shouldincrease their knowledge of number by periodically questioning whetherthe selection of denary numeric symbols used by the contestant wouldchange if the game takes the unique values of the value block piecesinto consideration.

Yet a fourth version of this game can be played by two or more people.Each player will take a turn being a contestant and a referee. Thecontestant with the lowest points total wins the game.

In this version, each contestant starts with a score of ten. The refereeinstructs the contestant to throw all value blocks on the floor. Onepoint is added to the contestant's score for every value block whose topface is blank. Only the value blocks whose top face is not blank will beplaced on the numeric grid. The referee starts the clock to record theamount of time it takes the contestant to unscramble the value blocksand place them in their rightful position on the numeric grid. Thecontestant signals to the referee to stop the clock when he or shethinks the value blocks have been assembled correctly. If the contestantis wrong, he or she is cautioned and five penalty points are added. Thereferee will continue timing the contestant until all of the valueblocks are assembled onto their rightful positions on the numeric grid.The contestant's finishing time and points score are recorded. When allplayers have been a contestant, the player with the fastest time trialgets ten bonus points deducted from his or her score. If more than oneplayer has the lowest final score, that contestant with the fewestpenalty points is declared the winner. If there is no clear winner afterconsidering the penalty points, that contestant with the most valueblocks on the numeric grid is declared the winner. In the event thatthere still remains a tie after considering the number of value blockson the numeric grid, the contestant with the ten bonus points isdeclared the winner.

There is a plurality of games that can be played with the device,including but not limited to manual games, computer games, games overthe internet and games using mobile telephony. The game board can beeasily designed and adapted using computer programming and made suitablefor software application on various operating system platforms. Gameversions that have chance elements associated with the value blockpieces can be simulated with random generators or probability basedalgorithms. Notwithstanding, there are countless iterations of thedevice and games played using the device that can be created andrecreated for teaching and learning of numeric symbols and numeralsystems.

What is claimed:
 1. A device for teaching and learning numeral systemscomprising at least one game board and a plurality of value block pieceshaving at least three sides, wherein for a base ten numeral system, thegame board comprises seven numeric columns to the left of a decimalpoint column and three numeric columns to the right of the decimal pointcolumn, and wherein each numeric column has ten rows, the first row ofwhich has insignia “0” representing the numeric symbol 0; the second row“1”; the third row “2”; the fourth row “3”; the fifth row “4”; the sixthrow “5”; the seventh row “6”; the eighth row “7”; the ninth row “8”; andthe tenth row “9” and wherein there is equal spacing between the numericsymbols to form a numeric grid thereon, and wherein each value blockpiece identifies the number equivalent value of a numeric symbol derivedfrom the symbol's location on the numeric grid.
 2. The device of claim1, wherein the description label for each numeric column is the placevalue position relative to the decimal point column and is written onthe numeric grid just above the insignia for the denary numeric symbolsand the description labels for the ten numeric columns are from left toright: “unit millions place”; “hundred thousands place”; “ten thousandsplace”; “unit thousands place”; “hundreds place”; “tens place”; “unitsplace”; “tenths place”; “hundredths place”; and “thousandths place”. 3.The device of claim 1, wherein the description label for each numericcolumn is the place value position relative to the decimal point columnand is written on the numeric grid just above the insignia for thedenary numeric symbols and the standard form labels for the ten numericcolumns are from left to right: “10⁶ place”; “10⁵ place”; “10⁴ place”;“10³ place”; “10² place”; “10¹ place”; “10⁰ place”; “10⁻¹ place”; “10⁻²place”; and “10³ place”.
 4. The device of claim 1, wherein the numericgrid is truncated to include only those numeric symbols applicable forother numeral base systems.
 5. The device of claim 1, wherein thenumeric grid comprises numeric symbols written in the negative todelineate negative numbers.
 6. The device of any one of claim 1, 2 or 3,wherein the value block piece is a cuboid having a first side, secondside, third side, fourth side, fifth side and sixth side.
 7. The deviceof claim 6, wherein the first side of each cuboid value block hasinsignia “0”, “1”, “2”, “3”, “4”, “5”, “6”, “7”, “8” or “9”, andwherein, the second side is opposite the first side and is left blankand wherein the third side of each value block has written in numberlanguage words the place position of the numeric symbol and wherein thefourth side which is opposite to the third side of each value block isthe value of the numeric symbol written as a decimal number and whereinthe fifth side of each value block is the value of the numeric symbolwritten in standard form and wherein the sixth side of each value blockis the value of the numeric symbol written as the numeric symbolmultiplied by (or divided by in the case decimals) the ordinary numberexpansion of the standard form label.
 8. The device of claim 1, whereinthe value block is a three sided solid figure.